WittVectors : Index

• baseMap (missing documentation)
• baseMap(WittRingMap) -- Returns the underlying RingMap of a WittRingMap
• createEquations -- Finds explicit equations satisfied by the parameters of a Frobenius lift up to a given degree
• createEquations(...,Homogeneous=>...) -- Finds explicit equations satisfied by the parameters of a Frobenius lift up to a given degree
• createEquations(...,PerturbationTerm=>...) -- Finds explicit equations satisfied by the parameters of a Frobenius lift up to a given degree
• explicit (missing documentation)
• explicit(WittIdeal) -- Obtains the explicit version of a WittIdeal.
• explicit(WittPolynomialRing) -- Expresses a WittPolynomialRing as a finitely generated algebra over the integers.
• explicit(WittQuotientRing) -- Expresses a WittQuotientRing as a finitely generated algebra over the integers.
• findFrobeniusLift -- Finds a random lift of the Frobenius
• findFrobeniusLift(...,Homogeneous=>...) -- Finds a random lift of the Frobenius
• findFrobeniusLift(...,Nontrivial=>...) -- Finds a random lift of the Frobenius
• findFrobeniusLift(...,PerturbationTerm=>...) -- Finds a random lift of the Frobenius
• findFrobeniusLift(...,Verbose=>...) -- Finds a random lift of the Frobenius
• findFrobeniusLiftConstraints -- Finds the equations satisfied by a delta structure on a ring R
• findFrobeniusLiftConstraints(...,Homogeneous=>...) -- Finds the equations satisfied by a delta structure on a ring R
• findFrobeniusLiftConstraints(...,PerturbationTerm=>...) -- Finds the equations satisfied by a delta structure on a ring R
• fSplittingHeight -- Finds the quasi-F-split height ht(S/I) of the quotient of the polynomial ring S=(ZZ/p)[x1,...,xn] by an ideal I generated by a regular sequence (f1,...,fm).
• fSplittingHeight(...,MaxHeight=>...) -- Finds the quasi-F-split height ht(S/I) of the quotient of the polynomial ring S=(ZZ/p)[x1,...,xn] by an ideal I generated by a regular sequence (f1,...,fm).
• generators(WittIdeal) -- Extract the generators of a WittIdeal.
• makeCoefficientFieldPrime (missing documentation)
• MaxHeight (missing documentation)
• Nontrivial (missing documentation)
• overring (missing documentation)
• overringMap (missing documentation)
• PerturbationTerm (missing documentation)
• ring(WittRingElement) -- Returns the Witt ring that a WittRingElement belongs to
• toList(WittRingElement) -- Converts a WittRingElement into a List
• truncate(ZZ,WittPolynomialRing) -- Crop Witt ring to the ring of Witt vectors of a given length
• truncate(ZZ,WittQuotientRing) -- Crop Witt Quotient ring to the ring of Witt vectors of a given length
• truncate(ZZ,WittRingElement) -- Crop Witt Vector to have a given length.
• truncation (missing documentation)
• unWitt -- Returns the underlying ring R of a Witt ring W_n(R)
• unWitt(WittPolynomialRing) -- Returns the underlying ring R of a Witt ring W_n(R)
• unWitt(WittQuotientRing) -- Returns the underlying ring R of a Witt ring W_n(R)
• verschiebung (missing documentation)
• verschiebung(WittRingElement) -- The Verschiebung map on an element
• witt (missing documentation)
• witt(List) -- Forms a WittRingElement from a list of ring elements
• witt(ZZ,PolynomialRing) -- Builds a Witt ring.
• witt(ZZ,QuotientRing) -- Forms the n-th Witt ring of a quotient ring
• witt(ZZ,RingMap) -- The map induced on Witt rings by a RingMap.
• witt(ZZ,ZZ,RingMap) -- The map induced on Witt rings by a RingMap.
• wittFrobenius (missing documentation)
• wittFrobenius(WittPolynomialRing) -- The (Witt) Frobenius map of a Witt ring
• wittFrobenius(WittQuotientRing) -- The (Witt) Frobenius map of a Witt ring
• wittFrobenius(WittRingElement) -- The (Witt) Frobenius map on an element
• wittFrobenius(ZZ,Ring) -- The (Witt) Frobenius map on the Witt vectors of a ring
• wittGenerators (missing documentation)
• WittIdeal -- Ideals in Witt rings.
• wittIdeal -- Make an ideal in a Witt ring.
• wittIdeal(List) -- Make an ideal in a Witt ring.
• wittIdeal(Sequence) -- Make an ideal in a Witt ring.
• wittIdeal(WittRingElement) -- Make an ideal in a Witt ring.
• wittLength -- Returns the length of the Witt vectors in a given Witt ring
• wittLength(WittPolynomialRing) -- Returns the length of the Witt vectors in a given Witt ring
• wittLength(WittQuotientRing) -- Returns the length of the Witt vectors in a given Witt ring
• WittOverring (missing documentation)
• wittOverring -- Returns the n-th WittOverring of a ring R, or the overring of a witt ring.
• wittOverring(WittPolynomialRing) -- Returns the n-th WittOverring of a ring R, or the overring of a witt ring.
• wittOverring(WittQuotientRing) -- Returns the n-th WittOverring of a ring R, or the overring of a witt ring.
• wittOverring(ZZ,Ring) -- Returns the n-th WittOverring of a ring R, or the overring of a witt ring.
• wittOverringIdeal -- The expansion of the witt ideal to the witt overring.
• wittOverringIdeal(ZZ,Ideal) -- The expansion of the witt ideal to the witt overring.
• wittOverringToTuple -- Converts an element of the explicit overring of a Witt ring into a tuple.
• WittPolynomialRing -- The class of the n-th Witt ring of a polynomial ring.
• WittQuotientRing -- The class of the n-th Witt ring of a quotient of a polynomial ring.
• WittRing (missing documentation)
• WittRingElement -- The Type for elements of WittPolynomialRing and WittQuotientRing.
• WittRingElement * WittRingElement -- Multiplication of WittRingElements.
• WittRingElement + WittRingElement -- Addition of WittRingElements.
• wittRingIdeal -- Returns the n-th witt ideal in explicit form.
• wittRingIdeal(ZZ,Ideal) -- Returns the n-th witt ideal in explicit form.
• WittRingMap -- The class of maps between Witt rings.
• wittRingToTuple -- Converts an element of the explicit presentation of a Witt ring into a tuple.
• wittSub (missing documentation)
• wittTupleToOverring -- Converts an element of a Witt ring to an element of the overring of its explicit presentation.
• wittTupleToRing -- Converts an element of a Witt ring to an element of its explicit presentation.
• WittVectors -- computations with finite-length Witt vectors